There are a few routes, IMO this is the most direct, using main roads, mostly with bus lanes, with as few turns as possible. It will take you less than a hour as follows:
Leave via the main entrance steps at Waterloo,
turn left, go over the IMAX roundabout,
Follow the A3200 Stamford Street - Southwark Street until you get to London Bridge. You will have to do a quick left / right on to Tooley Street.
Then take A200 Tooley Street - Jamaica Road, when you get to a big roundabout at the Rotherhithe tunnel, take the third exit to Lower Road, follow your nose to Evelyn Street and Creek Road. This takes you to Greenwich.
Go straight through the Greenwich one way system.
Then take the A206 Trafalagar Road. After about a mile you will get to a cross roads with traffic lights.
Turn left at traffic lights on to A2203 Blackwall Lane.
The O2 will be well sign posted, when you get to the big roundabout .
Good luck